Multiple realities
(covers information from several alternate timelines)

Saru with threat ganglia extended

Threat ganglia were five pairs of tendrils that extended from the base of a Kelpien's head when they sensed danger. They worked by responding to shifts in the environment, thus acting as an early warning system. Their presence made empathy a defining trait of the species. (DIS: "An Obol for Charon")

The vahar'ai was marked by the ganglia inflaming in a manner not otherwise seen. Eventually, they came loose, ending the condition. (DIS: "An Obol for Charon")

Ganglia were not the only method a Kelpien had for sensing potentially dangerous individuals and situations. As Saru commented in 2257, even without his ganglia, he still could strongly sense such things intuitively. (DIS: "The Red Angel")

Notable activations

In 2256, Saru's threat ganglia extended in the prelude to the Battle of the Binary Stars, when the Sarcophagus decloaked. (DIS: "The Vulcan Hello") After the battle, his ganglia began reacting to the presence of Michael Burnham, as he now considered her dangerous – for example, when Burnham did not leave the USS Discovery on prison shuttle SPT 21 and when he realized she had instead been given the opportunity to remain aboard the ship. (DIS: "Context Is for Kings", "The Butcher's Knife Cares Not for the Lamb's Cry") Burnham remarked that his threat ganglia were indicating he hadn't been consulted in this decision and that, since she was only there to be of assistance, he could tell his threat ganglia to relax, though he replied that they still weren't convinced. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")

However, as Burnham also noticed, Saru's threat ganglia did not extend in the presence of "Ripper", which Burnham interpreted as evidence that the animal was not innately dangerous. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")

Following Discovery's arrival into the mirror universe, Saru's threat ganglia extended when Lieutenant Ash Tyler, later revealed to be the Klingon sleeper agent Voq, entered the bridge. (DIS: "Despite Yourself", "The Wolf Inside")

In the mirror universe, Kelpiens' threat ganglia was considered a treat when cooked. Emperor Philippa Georgiou fed one, taken from a slave, to Michael Burnham. (DIS: "Vaulting Ambition")

Learning that who he knew as Captain Gabriel Lorca was actually his mirror counterpart from the Terran Empire, Saru was bemused as to how his threat ganglia never reacted to him. (DIS: "What's Past Is Prologue")

Saru's threat ganglia extended as the Discovery approached Starbase 1; once Discovery dropped out of warp, it was found that the starbase had been seized by the House of D'Ghor. (DIS: "The War Without, The War Within")

Saru's threat ganglia fell out when he reached vahar'ai. (DIS: "An Obol for Charon") Afterwards, however, similar protrusions activated when Saru was cornered by a Ba'ul, and they shot darts at the individual. Soon thereafter, Saru's sister, Siranna, and all other Kelpiens on their homeworld of Kaminar experienced their own threat ganglia falling out when they too underwent vahar'ai. (DIS: "The Sound of Thunder")

Ganglia is the plural of ganglion, which is a grouping of nerve cells.
The placement of the threat ganglia in a Kelpien's anatomy underwent much revision. Explained Star Trek author David Mack, "From the original story outline documents to how they executed the prosthetics, [the threat ganglia] changed dramatically. Like, originally, they were on one part of his head, then they moved to a different part of his head. Now they're behind his ears." [1]
The threat ganglia (when not used as food) were depicted using CGI and were the only digitally enhanced part of the makeup involved in portraying Saru. "They kind of come [off] the back of my head, back in here somewhere, around the back, behind the ear somewhere," stated Saru actor Doug Jones. "We hadn't really seen what they look like exactly yet because I have to mime them, whenever I pop them back in." [2]
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